I have a female betta in a 5 gallon tank, who used to have 4 other tankmates, until they died due to my heater breaking, them not having any heaters small enough at the store so having to special order one, and them not being as hardy as my betta.
So, I have a working heater again and I'm ready to restock the tank.
However, when I bought a phantom tetra, my female betta harassed it to the point of it jumping out the tank and onto my desk. Not kidding. -___- So I quarantined the poor guy, but of course I can't put him back in the betta tank and he can't stay in quarantine forever.

My other tanks are a 2 gallon with a neon tetra and one of those glow-fish in it, and I have two male bettas which, obviously, I can't put the tetra with.

So, my questions are:
-What are some better suited tankmates for my female betta? (And don't say a snail or something. I mean a fish.)
-What do I do with my poor phantom tetra?

Also, I heard about something called the "Home field" advantage. My betta was placed in the tank, originally AFTER her tankmates. So she probably is being territorial now that she has the tank to herself. Should I take her out and put HER in quarantine, then put my phantom tetra in, wait a day or so, then put her back in?

There are no fish that should go in a 5 gallon besides the betta. There are some micro species but they have to be special ordered most of the time, and they would have to be the only things in the tank. And just a side note, neons are schooling fish that do best with 5 friend and require a 10gallon tank, same goes for the glo-fish. But they are a danio hybrid that require 20 gallons for swimming requirements.

There are no fish that should go in a 5 gallon besides the betta. There are some micro species but they have to be special ordered most of the time, and they would have to be the only things in the tank. And just a side note, neons are schooling fish that do best with 5 friend and require a 10gallon tank, same goes for the glo-fish. But they are a danio hybrid that require 20 gallons for swimming requirements.

I agree, no tank mates except snails or shrimp in anything less than 10 gallons.

Also, I heard about something called the "Home field" advantage. My betta was placed in the tank, originally AFTER her tankmates. So she probably is being territorial now that she has the tank to herself. Should I take her out and put HER in quarantine, then put my phantom tetra in, wait a day or so, then put her back in?

You can't put the phantom tetra in there, you need to take it back to the store. If you choose to not take it back to the store, you will need to buy the tetra at least a ten gallon tank and four other phantom tetras.